Preheat smoker to 250°F (121°C).
Quarter the tomatoes, then toss in baking dish with oil, salt, and pepper.
Slice both garlic bulbs along their equator, place all parts in two foil boats. Drizzle oil and sprinkle salt and pepper on both.
Place tomatoes and garlic in smoker for 2 hours total. Smoke the garlic uncovered for the first 15 – 20 minutes, then drizzle more oil on top and cover tightly with foil.
After 2 hours have passed, take tomatoes and garlic out of smoker and allow to cool. Peel skins from tomatoes, remove seeds, and squeeze garlic into a small bowl.
Chop onion, carrot, and celery (or use 2 to 3 bags of frozen mirepoix).
Cook onion, carrot, and celery in butter or oil until the vegetables sweat.
Add garlic and tomato paste and stir together.
Add peeled tomatoes, canned bell pepper, vegetable stock, and herbs. Bring to a boil and then reduce to a simmer for 20 – 30 minutes. Remove basil and bay leaves at the end of this.
Use an immersion blender and/or standing blender and blend soup until completely smooth.
Return blended soup to pot and stir in heavy cream.
Serve with a basil garnish and with a side of crusty bread or a grilled cheese sandwich.